I can't get consistent 4K/60 with a GTX1080 in a lot of games not without compromising on quality settings.

I think we're saying the same thing. Stuff like Warframe, LoL, PoE, Overwatch will be doable at 4K on the 2060. Even BFV and FC5 get close to 4K/60 in benchmarks. 4K/30 or low-med settings is more realistic.

The 2060 does get very close to the 1080 btw.

Personally if I was buying a PC moniter/setup now. I'd aim for a 1080p 144hz screen. Becuase they are much better value, easier to drive and the increase to 1440p/4K isn't necessarily worth it imo. I purchased a 1440p screen 3 1/2 yrs ago and kinda regret it now. Some of the prices on decent 1440p/4K PC monitors is worse than the GPU premium.